Lottery expected value calculator
Is the lottery ever worth playing? Expected value answers it: the average amount a ticket returns compared with its price. Enter the jackpot, tax and chance of sharing and see what a ticket is really worth.
Expected value per ticket
$0.513
from smaller prizes $0.320 + jackpot $0.193
Net after the ticket price
-$1.487
you lose this on average
Return on each dollar
25.6%
what comes back on average
Expected value is an average over many plays, not a prediction. Even if a very large jackpot made the average look better, taxes, sharing and the cash option usually remove the edge, and the realistic outcome of any single ticket is still losing it.
How expected value works
Expected value is the sum of each prize multiplied by its probability. For the lottery, add up the smaller prizes (a fixed amount per ticket for any given game) and the jackpot term: the chance of winning times the after-tax cash value, divided by the number of people you expect to share it with. Subtract the ticket price to get your average profit or loss.
Why a big jackpot rarely makes it positive
Even when the headline jackpot is very large, the expected value per ticket is usually below the price once these are included.
- The cash option is about half the advertised jackpot.
- Tax can take 35% to 45% of the cash.
- Bigger jackpots sell more tickets, so you are more likely to share.
- Smaller prizes are worth much less per ticket than the price.
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Frequently asked questions
Is Powerball ever positive expected value?
On paper the headline numbers can look positive at extreme jackpots, but after the cash option, tax and prize sharing, it almost never is.
What is a good expected value?
Zero or above means you would not lose on average. Lotteries are below zero. The closer to the price, the better the value.
Why does sharing matter?
When many tickets are sold, several people may pick the winning numbers and split the prize, which cuts your share.
Can I use this for other lotteries?
Yes. Choose "Any other lottery" and enter the jackpot odds and the average value of smaller prizes.